Polymer Science, Series C

, Volume 60, Supplement 1, pp 18–24 | Cite as

Self-Consistent Field Modeling of Homopolymers at Interfaces in the Long Chain Length Limit

  • F. A. M. LeermakersEmail author


According to de Gennes, the density profile for homopolymers adsorbing onto planar surfaces is characterized by a proximal, central and distal region. We have used self-consistent field calculations and focused on the central region in the limit of very long chain lengths. Our results complement earlier predictions for comparatively low molecular weights that basically only revealed a mean field scaling exponent of −2 for the power-law decay of the density. For very long chains, however, a more rich picture emerges. Apart from an inner sub-region where the loop conformations dominate and still the mean field exponent is found, there exists an outer sub-region where the tail conformations dominate with excluded volume scaling of ‒4/3. It is shown that the outer region grows logarithmically with chain length and only will exceed the decade when the length of the polymer chains exceeds N ≈ 3 × 107. We argue that ‘inner-adsorption blobs’ are visited twice by loop conformations (loops by definition return to the surface) and hence become overcrowded giving rise to mean field scaling. The ‘outer-adsorption blobs’ are visited just once by tails (tails do not need to return to the surface) and therefore provide the expected excluded volume scaling.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. A. Fleer, M. A. Cohen Stuart, J. M. H. M. Scheutjens, T. Cosgrove, and B. Vincent, Polymers at Interfaces (Chapman and Hall, London, 1993).Google Scholar
  2. 2.
    P.-G. de Gennes, Macromolecules 14, 1637 (1981).CrossRefGoogle Scholar
  3. 3.
    P.-G. de Gennes, Macromolecules 15, 492 (1982).CrossRefGoogle Scholar
  4. 4.
    P.-G. de Gennes, Adv. Colloid Interface Sci. 27, 189 (1987).CrossRefGoogle Scholar
  5. 5.
    F. A. M. van der Linden and F. A. M. Leermakers, Macromolecules 25, 3449 (1992).CrossRefGoogle Scholar
  6. 6.
    L. Auvray and J. P. Cotton, Macromolecules 20, 202 (1987).CrossRefGoogle Scholar
  7. 7.
    T. Cosgrove, T. L. Crowley, B. Vincent, A. W. Burgess, T. L. Croley, T. King, J. D. Turner, and T. F. Tadros, Polym. Commun. 22, 283 (1981).CrossRefGoogle Scholar
  8. 8.
    T. Cosgrove, T. L. Crowley, B. Vincent, K. G. Barnett, and T. F. Tadros, Faraday Symp. Chem. Soc. 16, 101 (1981).CrossRefGoogle Scholar
  9. 9.
    J. C. Marshall, T. Cosgrove, F. A. M. Leermakers, T.M. Obey, and C. A. Dreiss, Langmuir 20, 4480 (2004).CrossRefGoogle Scholar
  10. 10.
    J. H. M. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 83, 1619 (1979).CrossRefGoogle Scholar
  11. 11.
    J. H. M. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 84, 178 (1980).CrossRefGoogle Scholar
  12. 12.
    S. F. Edwards, Proc. Phys. Soc. (London) 85, 613 (1965).CrossRefGoogle Scholar
  13. 13.
    O. A. Evers, J. M. H. M. Scheutjens, and G. J. Fleer, Macromolecules 23, 5221 (1990).CrossRefGoogle Scholar
  14. 14.
    I. M. Lifshits, A. Yu. Grosberg, and A. R. Khokhlov, Rev. Mod. Phys. 50, 683 (1978).CrossRefGoogle Scholar
  15. 15.
    J. M. H. M. Scheutjens, G. J. Fleer, and M. A. Cohen Stuart, Colloids Surf. 21, 285 (1986).CrossRefGoogle Scholar
  16. 16.
    A. N. Semenov and J. F. Joanny, Europhys. Lett. 29, 279 (1995).CrossRefGoogle Scholar
  17. 17.
    A. N. Semenov, J. B. Avalos, A. Johner, and J. F. Joanny, Macromolecules 29, 2179 (1996).CrossRefGoogle Scholar
  18. 18.
    D. W. Schaefer, Polymer 25, 387 (1984).CrossRefGoogle Scholar
  19. 19.
    B. R. Postmus, F. A. M. Leermakers, and M. A. Cohen Stuart, Langmuir 24, 1930 (2008).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Physical Chemistry and Soft MatterWageningen University and ResearchWageningenthe Netherlands

Personalised recommendations